Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
296 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C4×#3624 | C4 | semidirect |
| 12. C4×#3624 | C4 | semidirect |
| 13. C4×C8×C17 | C4 | semidirect |
| 14. C8×Dic17 | C4 | semidirect |
| 15. C4×#3622 | C4 | semidirect |
| 23. C4×#595 | C8 | semidirect |
| 78. C4×C8 | #595 | semidirect |
| 79. C17 | #1744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#63242 | 2 |
| C42×#595 | 2 |
| #11763674 | 2 |
| C4×C8×D17 | 2 |
| #1744 | 17 |